Numeric.MixedTypes.Field

Field

type CanAddSubMulDivBy t s = (CanAddSubMulBy t s, CanDivBy t s)

type Field t = (Ring t, CanDivSameType t, CanRecipSameType t, CanAddSubMulDivBy t Rational, CanAddSubMulDivBy t Integer, CanAddSubMulDivBy t Int)

type CertainlyEqField t = (Field t, CertainlyEqRing t)

type OrderedField t = (Field t, OrderedRing t, HasOrder t Rational)

type OrderedCertainlyField t = (CertainlyEqField t, OrderedCertainlyRing t, HasOrderCertainly t Rational)

Division

class CanDiv t1 t2 where

A replacement for Prelude's binary /. If t1 = t2 and Fractional t1, then one can use the default implementation to mirror Prelude's /.

Associated Types

type DivType t1 t2

Methods

divide :: t1 -> t2 -> DivType t1 t2

divide :: (DivType t1 t2 ~ t1, t1 ~ t2, Fractional t1) => t1 -> t1 -> t1

Instances

CanDiv Double Double

Associated Types

type DivType Double Double :: *

Methods

divide :: Double -> Double -> DivType Double Double

CanDiv Double Int

Associated Types

type DivType Double Int :: *

Methods

divide :: Double -> Int -> DivType Double Int

CanDiv Double Integer

Associated Types

type DivType Double Integer :: *

Methods

divide :: Double -> Integer -> DivType Double Integer

CanDiv Double Rational

Associated Types

type DivType Double Rational :: *

Methods

divide :: Double -> Rational -> DivType Double Rational

CanDiv Int Double

Associated Types

type DivType Int Double :: *

Methods

divide :: Int -> Double -> DivType Int Double

CanDiv Int Int

Associated Types

type DivType Int Int :: *

Methods

divide :: Int -> Int -> DivType Int Int

CanDiv Int Integer

Associated Types

type DivType Int Integer :: *

Methods

divide :: Int -> Integer -> DivType Int Integer

CanDiv Int Rational

Associated Types

type DivType Int Rational :: *

Methods

divide :: Int -> Rational -> DivType Int Rational

CanDiv Integer Double

Associated Types

type DivType Integer Double :: *

Methods

divide :: Integer -> Double -> DivType Integer Double

CanDiv Integer Int

Associated Types

type DivType Integer Int :: *

Methods

divide :: Integer -> Int -> DivType Integer Int

CanDiv Integer Integer

Associated Types

type DivType Integer Integer :: *

Methods

divide :: Integer -> Integer -> DivType Integer Integer

CanDiv Integer Rational

Associated Types

type DivType Integer Rational :: *

Methods

divide :: Integer -> Rational -> DivType Integer Rational

CanDiv Rational Double

Associated Types

type DivType Rational Double :: *

Methods

divide :: Rational -> Double -> DivType Rational Double

CanDiv Rational Int

Associated Types

type DivType Rational Int :: *

Methods

divide :: Rational -> Int -> DivType Rational Int

CanDiv Rational Integer

Associated Types

type DivType Rational Integer :: *

Methods

divide :: Rational -> Integer -> DivType Rational Integer

CanDiv Rational Rational

Associated Types

type DivType Rational Rational :: *

Methods

divide :: Rational -> Rational -> DivType Rational Rational

CanDiv a b => CanDiv [a] [b]

Associated Types

type DivType [a] [b] :: *

Methods

divide :: [a] -> [b] -> DivType [a] [b]

CanDiv a b => CanDiv (Maybe a) (Maybe b)

Associated Types

type DivType (Maybe a) (Maybe b) :: *

Methods

divide :: Maybe a -> Maybe b -> DivType (Maybe a) (Maybe b)

type CanDivBy t1 t2 = (CanDiv t1 t2, DivType t1 t2 ~ t1)

type CanDivSameType t = CanDivBy t t

type CanRecip t = CanDiv Integer t

type CanRecipSameType t = (CanDiv Integer t, DivType Integer t ~ t)

(/) :: CanDiv t1 t2 => t1 -> t2 -> DivType t1 t2

recip :: CanRecip t => t -> DivType Integer t

powUsingMulRecip :: (CanBeInteger e, CanRecipSameType t, CanMulSameType t, ConvertibleExactly Integer t) => t -> e -> t

Tests

specCanDiv :: (CanRecip t1, CanRecip (DivType Integer t1), Show (DivType Integer (DivType Integer t1)), HasEqCertainly t1 (DivType Integer (DivType Integer t1)), CanTestZero (DivType Integer t1), CanDivX t1 t2, CanTestZero t1, CanTestZero t2, CanDivX t1 t1, CanMulX t1 (DivType t1 t2), ConvertibleExactly Integer t2, ConvertibleExactly Integer t1) => T t1 -> T t2 -> Spec

HSpec properties that each implementation of CanDiv should satisfy.

specCanDivNotMixed :: (CanRecip t, CanRecip (DivType Integer t), Show (DivType Integer (DivType Integer t)), HasEqCertainly t (DivType Integer (DivType Integer t)), CanTestZero (DivType Integer t), CanDivX t t, CanTestZero t, CanMulX t (DivType t t), ConvertibleExactly Integer t) => T t -> Spec

HSpec properties that each implementation of CanDiv should satisfy.

type CanDivX t1 t2 = (CanDiv t1 t2, Show t1, Arbitrary t1, Show t2, Arbitrary t2, Show (DivType t1 t2), HasEqCertainly t1 (DivType t1 t2))

Compound type constraint useful for test definition.